HALLEY 



43 



of the given number of years is —■ ; the chance that the younger 



Till 



will be alive and the elder dead is -r^ ; and so on. 



Halley gives according to the fashion of the time a geometri- 

 cal illustration. 



D 

 1 



B 



E _C 



G 



H 



Let AB or CD represent N, and DE or BH represent R, 

 so that EC or HA represents F. Similarly AC, AF, CF may 

 represent n, r, y. Then of course the rectangle ECFG represents 

 Ty, and so on. 



In like manner, Halley first gives the proposition relating to 

 three lives in an algebraical form, and then a geometrical illus- 

 tration by means of a parallelepiped. We find it difficult in 

 the present day to understand how such simple algebraical pro- 

 positions could be rendered more intelligible by the aid of areas 

 and solids. 



67. On pages 654^ — 6oQ of the same volume of the Pliiloso- 

 pMcal Transactions we have Some further Considerations on the 

 Breslaiu Bills of Mortality. By the same Hand, d'C. 



68. De Moivre refers to Halley's memoir, and republishes 

 the table; see Be Moivre's Doctrine of Chances, pages 261, ^^o. 



